{
  "id": "1105.3952",
  "version": "v2",
  "published": "2011-05-19T18:20:18.000Z",
  "updated": "2012-04-10T18:08:32.000Z",
  "title": "The Automorphism Groups of a Family of Maximal Curves",
  "authors": [
    "Robert Guralnick",
    "Beth Malmskog",
    "Rachel Pries"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "The Hasse Weil bound restricts the number of points of a curve which are defined over a finite field; if the number of points meets this bound, the curve is called maximal. Giulietti and Korchmaros introduced a curve C_3 which is maximal over F_{q^6} and determined its automorphism group. Garcia, Guneri, and Stichtenoth generalized this construction to a family of curves C_n, indexed by an odd integer n greater than or equal to 3, such that C_n is maximal over F_{q^{2n}}. In this paper, we determine the automorphism group Aut(C_n) when n > 3; in contrast with the case n=3, it fixes the point at infinity on C_n. The proof requires a new structural result about automorphism groups of curves in characteristic p such that each Sylow p-subgroup has exactly one fixed point. MSC:11G20, 14H37.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-10T18:08:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "14H37"
    ],
    "keywords": [
      "automorphism group",
      "maximal curves",
      "hasse weil bound restricts",
      "finite field",
      "points meets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.3952G"
    }
  }
}